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The angular separation between the vectors A = 4i + 3j + 5k and B = i – 2j + 2k is (in degrees)
- a)65.8
- b)66.8
- c)67.8
- d)68.8
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
The angular separation between the vectors A = 4i + 3j + 5k and B = i ...
The dot product the vector is 8. Angle of separation is cos θ = 8/ (7.07 X 3) = 0.377 and θ = cos-1(0.377) = 67.8.
Most Upvoted Answer
The angular separation between the vectors A = 4i + 3j + 5k and B = i ...
To find the angular separation between two vectors A and B, we can use the dot product formula:
A · B = |A| |B| cosθ
where A · B is the dot product of A and B, |A| is the magnitude of vector A, |B| is the magnitude of vector B, and θ is the angle between the two vectors.
First, let's calculate the magnitudes of vectors A and B:
|A| = √(4^2 + 3^2 + 5^2) = √(16 + 9 + 25) = √50 = 5√2
|B| = √(1^2 + 0^2 + 0^2) = √(1 + 0 + 0) = √1 = 1
Next, let's calculate the dot product of A and B:
A · B = (4)(1) + (3)(0) + (5)(0) = 4
Now, we can substitute the values into the dot product formula to find the angle:
4 = (5√2)(1) cosθ
cosθ = 4 / (5√2)
θ = arccos(4 / (5√2))
Using a calculator, we find that θ is approximately 27.13 degrees.
Therefore, the angular separation between vectors A and B is approximately 27.13 degrees.
A · B = |A| |B| cosθ
where A · B is the dot product of A and B, |A| is the magnitude of vector A, |B| is the magnitude of vector B, and θ is the angle between the two vectors.
First, let's calculate the magnitudes of vectors A and B:
|A| = √(4^2 + 3^2 + 5^2) = √(16 + 9 + 25) = √50 = 5√2
|B| = √(1^2 + 0^2 + 0^2) = √(1 + 0 + 0) = √1 = 1
Next, let's calculate the dot product of A and B:
A · B = (4)(1) + (3)(0) + (5)(0) = 4
Now, we can substitute the values into the dot product formula to find the angle:
4 = (5√2)(1) cosθ
cosθ = 4 / (5√2)
θ = arccos(4 / (5√2))
Using a calculator, we find that θ is approximately 27.13 degrees.
Therefore, the angular separation between vectors A and B is approximately 27.13 degrees.
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